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August 2021 A Central Limit Theorem for incomplete U-statistics over triangular arrays
Matthias Löwe, Sara Terveer
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Braz. J. Probab. Stat. 35(3): 499-522 (August 2021). DOI: 10.1214/20-BJPS492

Abstract

We analyze the fluctuations of incomplete U-statistics over a triangular array of independent random variables. We give criteria for a Central Limit Theorem (CLT, for short) to hold in the sense that we prove that an appropriately scaled and centered version of the U-statistic converges to a normal random variable. Our method of proof relies on a martingale CLT. An application, a CLT for the hitting time for random walks on random graphs, will be presented in Löwe and Terveer (2020).

Acknowledgments

Research of both authors was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy EXC 2044-390685587, Mathematics Münster: Dynamics-Geometry-Structur.

Citation

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Matthias Löwe. Sara Terveer. "A Central Limit Theorem for incomplete U-statistics over triangular arrays." Braz. J. Probab. Stat. 35 (3) 499 - 522, August 2021. https://doi.org/10.1214/20-BJPS492

Information

Received: 1 July 2020; Accepted: 1 September 2020; Published: August 2021
First available in Project Euclid: 22 July 2021

Digital Object Identifier: 10.1214/20-BJPS492

Rights: Copyright © 2021 Brazilian Statistical Association

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Vol.35 • No. 3 • August 2021
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